The invention relates to systems for isolating resonating structures, and more particularly to a system for isolating a micromachined resonator.
Micromachined resonators are useful for creating light, compact, inexpensive, and durable inertial measurement systems, such as gyroscopes and accelerometers. Micromachined resonators are also finding broader application in other equipment dependent on a sustainable vibration rate, such as clocks. Because of their small size and light weight, micromachined resonators are particularly suitable for aerospace and outer space applications and it is anticipated that the use of micromachined resonators will expand.
As with other real world oscillating systems, micromachined resonators invariably experience some energy loss due to damping. For purposes of analysis, designers of micromachined resonators have traditionally assumed that the proof mass (m1) of an instrument was connected by a spring (k1) to a fixed, infinite mass, as shown schematically in FIG. 8A. A peripheral frame of the resonator, attached to a larger base was considered to be fixed because the base was attached to a much larger mass. The equation of motion for a system in which a mass is connected through a spring to an infinite mass is:
m1{umlaut over (x)}1+xcex31{dot over (x)}1+k1x1=D1ejxcfx89txe2x80x83xe2x80x83(1)
where m1 is the mass, xcex31 is the damping factor, and k1 is the spring constant. When solved for the Q (quality) factor of the system, the above equation yields the following solution:
Q=m1/xcex3xe2x80x83xe2x80x83(2)
Applicants realized upon experimentation, however, that the Q they measured did not correspond to that predicted by the above equation, indicating that the vibratory system was not as simple as previously thought. Although the frame was rigidly attached to the base, the connection between the base and the much larger mass was not entirely rigid. Thus, the proper model was not that of a single oscillating mass, but rather two separate masses and two springs as illustrated in FIG. 8B. The behavior of such a system is expressed as two simultaneous equations of motion, as follows:
m1{umlaut over (x)}1+k1(x1xe2x88x92x2)=D1ejwt; andxe2x80x83xe2x80x83(3)
m2{umlaut over (x)}2+k1(x2xe2x88x92x1)+k2x2+xcex32{dot over (x)}2=xe2x88x92D1ejxcfx89txe2x80x83xe2x80x83(4)
where m1 is the proof mass, m2 is the combined mass of the peripheral frame and the base, k1 is the spring constant of the spring system connecting the proof mass to the base, and k2 is constant of the spring-like system connecting the base to the fixed mass. When solved, the above two equations yield:                     Q        =                                                            (                                                      k                    2                                    -                                                            m                      2                                        ⁢                                          ω                      2                                                                      )                            2                        +                                          γ                2                2                            ⁢                              ω                2                                                          2            ⁢                          γ              2                        ⁢                          m              1                        ⁢                          πω              3                                                          (        5        )            
Thus, traditional methods of mounting the base of a resonator to a fixed mass, such as by glue or solder, behave like a relatively stiff (high k2) xe2x80x9csecond spring,xe2x80x9d leading to a low Q factor. More importantly, the characteristics of this effective spring cannot be accurately controlled, precluding optimization of system parameters to maximize the Q factor of the resonator. As shown in the solid-line curve of FIG. 9., which is a plot of Q vs. xcex32 for a typical two mass system, Q can be as low as 290, depending on the value of xcex32.
Additionally, prior art systems are vulnerable to vibration and temperature fluctuations, due largely to the nature of the connection between the base and the fixed mass to which it is mounted. Temperature changes, due to conduction across this connection can cause the micromachined semiconductor resonator to alter its shape and thus decrease the accuracy of the device.
The resonator of the invention addresses these problems by mounting the base to the fixed mass using a third spring system and thus mounting the base to the fixed mass through a relatively compliant isolation spring system of low spring constant (k2) and low damping (xcex32). This results in an effective three-mass system illustrated schematically in FIG. 8C, where the relatively stiff connection (k3xcex33) to the fixed mass is isolated from the motion of the resonator by the isolation spring system. The effect of the stiff mounting to the fixed mass is therefore minimized, greatly increasing the Q of the resonant system. The isolation spring system also enhances controllability of the Q through system design because the dominant spring characteristics, which are those of the first and second spring systems, can be accurately controlled.
Thus, a micromachined resonator constructed according to one embodiment of the invention includes a proof mass suspended by a first spring structure. The first spring structure is attached to a base structure which has a plurality of electrodes. The base structure is coupled to an external support structure by a second spring system that serves as a spring isolation system.
In one embodiment of the invention, the second spring structure includes at least one micromachined spring, although in alternative embodiments, a membrane can be substituted for the at least one micromachined spring. The number of micromachined springs and the attachment points of each micromachined spring is variable to control the rigidity, damping and balance of the isolation system. In an embodiment of the invention, the second spring structure contains two micromachined springs positioned on opposing locations of the base structure that couple the base structure to the external support structure.
In an alternative embodiment of the invention, the base structure has a rectangular frame, and the second spring structure has two micromachined springs coupling adjacent sides of the base structure to the external support structure. In another alternative embodiment of the invention, the base structure is a rectangular frame and the second spring structure has at least four micromachined springs coupling each of the four sides of the base structure to the external support structure. In yet another alternative embodiment of the invention, the second spring structure has one micromachined spring coupling the base structure to the external support structure.
Additionally, there may be two or more micromachined spring elements in parallel coupling a point on the base structure to a point on the external support structure. In one embodiment of the invention, the second spring structure comprises four sets of two micromachined spring elements substantially parallel to each other coupling the base structure to the external support structure. In an alternative embodiment, the second spring structure comprises four sets of four micromachined spring elements substantially parallel to each other coupling the base structure to the external support structure.
The length and shape of the each micromachined spring is variable to control the rigidity and damping of the isolation system. In one embodiment, the base structure is rectangular, and the second spring structure comprises four micromachined springs. Each micromachined spring is positioned from a corner of the base structure, around three sides of the base structure, to the external support structure.
The resonator with the spring isolation system can be used in many types of inertial measurement systems, such as gyroscopes and accelerometers. In one embodiment of the present invention, the base structure has drive circuitry for exciting a mode of the proof mass having a mode shape, bias circuitry for supplying a voltage to modify the mode shape, sensing circuitry for measuring acceleration by detecting a change of the mode shape of the proof mass; and output circuitry for outputting a signal indicating the acceleration. In an alternative embodiment, the base structure has sensing circuitry for measuring rotation by detecting a change of the mode shape of the proof mass; and output circuitry for outputting a signal indicating the rotation. In one embodiment of the invention, the supply of electricity to the circuitry in the base structure takes place through lead wires coupled to at least one micromachined spring of the second spring structure.
In an additional embodiment of the present invention, there is at least one additional structure coupled to the base structure, the second spring system coupling the at least one additional structure to the external support structure. In yet another additional embodiment, the second base is coupled by the second spring system to a third base. The third base is coupled to the external support structure by a third spring system functioning as an additional spring isolation system
A more complete understanding of the present invention can be obtained from the following detailed description and the accompanying drawings.